Suppose we wanted to use SAT math scores to estimate verbal scores based on the information in Exercise 53.
a) What is the correlation?
b) Write the equation of the line of regression predicting verbal scores from math scores.
c) In general, what would a positive residual mean in this context?
d) A person tells you her math score was 500. Predict her verbal score.
e) Using that predicted verbal score and the equation you created in Exercise 53, predict her math score.
f) Why doesn't the result in part e come out to 500?
In Exercise 53
The SAT is a test often used as part of an application to college. SAT scores are between 200 and 800, but have no units. Tests are given in both Math and Verbal areas. SAT-Math problems require the ability to read and understand the questions, but can a person's verbal score be used to predict the math score? Verbal and math SAT scores of a high school graduating class are displayed in the scatterplot, with the regression line added.

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800 700 i 600 500 400 400 500 600 700 800 Verbal SAT